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Full Description
This unique book addresses advanced linear algebra from a perspective in which invariant subspaces are the central notion and main tool. It contains comprehensive coverage of geometrical, algebraic, topological, and analytic properties of invariant subspaces. The text lays clear mathematical foundations for linear systems theory and contains a thorough treatment of analytic perturbation theory for matrix functions.
Contents
Preface to the Classics Edition
Preface to the First Edition
Introduction
Part One: Fundamental Properties of Invariant Subspaces and Applications. Chapter 1: Invariant Subspaces: Definitions, Examples, and First Properties
Chapter 2: Jordan Form and Invariant Subspaces
Chapter 3: Coinvariant and Semiinvariant Subspaces
Chapter 4 Jordan Form for Extensions and Completions
Chapter 5: Applications to Matrix Polynomials
Chapter 6: Invariant Subspaces for Transformations Between Different Spaces
Chapter 7: Rational Matrix Functions
Chapter 8: Linear Systems
Part Two: Algebraic Properties of Invariant Subspaces. Chapter 9: Commuting Matrices and Hyperinvariant Subspaces
Chapter 10: Description of Invariant Subspaces and Linear Transformation with the Same Invariant Subspaces
Chapter 11: Algebras of Matrices and Invariant Subspaces
Chapter 12: Real Linear Transformations
Part Three: Topological Properties of Invariant Subspaces and Stability. Chapter 13: The Metric Space of Subspaces
Chapter 14: The Metric Space of Invariant Subspaces
Chapter 15: Continuity and Stability of Invariant Subspaces
Chapter 16: Perturbations of Lattices of Invariant Subspaces with Restrictions on the Jordan Structure
Chapter 17: Applications
Part Four: Analytic Properties of Invariant Subspaces. Chapter 18: Analytic Families of Subspaces
Chapter 19: Jordan Form of Analytic Matrix Functions
Chapter 20: Applications
Appendix: List of Notations and Conventions
References
Author Index
Subject Index.
